TY - JOUR

T1 - Disordered Monomer-Dimer Model on Cylinder Graphs

AU - Dey, Partha S.

AU - Krishnan, Kesav

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023/8

Y1 - 2023/8

N2 - We consider the disordered monomer-dimer model on cylinder graphs Gn , i.e., graphs given by the Cartesian product of the line graph on n vertices, and a deterministic finite graph. The edges carry i.i.d. random weights, and the vertices also have i.i.d. random weights, not necessarily from the same distribution. Given the random weights, we define a Gibbs measure on the space of monomer-dimer configurations on Gn . We show that the associated free energy converges to a limit and, with suitable scaling and centering, satisfies a Gaussian central limit theorem. We also show that the number of monomers in a typical configuration satisfies a law of large numbers and a Gaussian central limit theorem with appropriate centering and scaling. Finally, for an appropriate height function associated with a matching, we show convergence to a limiting function and prove the Brownian motion limit around the limiting height function in the sense of finite-dimensional distributional convergence.

AB - We consider the disordered monomer-dimer model on cylinder graphs Gn , i.e., graphs given by the Cartesian product of the line graph on n vertices, and a deterministic finite graph. The edges carry i.i.d. random weights, and the vertices also have i.i.d. random weights, not necessarily from the same distribution. Given the random weights, we define a Gibbs measure on the space of monomer-dimer configurations on Gn . We show that the associated free energy converges to a limit and, with suitable scaling and centering, satisfies a Gaussian central limit theorem. We also show that the number of monomers in a typical configuration satisfies a law of large numbers and a Gaussian central limit theorem with appropriate centering and scaling. Finally, for an appropriate height function associated with a matching, we show convergence to a limiting function and prove the Brownian motion limit around the limiting height function in the sense of finite-dimensional distributional convergence.

KW - Central limit theorems

KW - Disordered systems

KW - Monomer-dimer models

KW - Random dimer activities

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U2 - 10.1007/s10955-023-03159-7

DO - 10.1007/s10955-023-03159-7

M3 - Article

AN - SCOPUS:85168455180

SN - 0022-4715

VL - 190

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 8

M1 - 146

ER -